Robust Quantum State Generation in Symmetric Spin Networks

TL;DR

This paper presents a robust control method for generating specific quantum states in symmetric spin networks, effectively compensating for electromagnetic field uncertainties using a moment quantization approach.

Contribution

It introduces a novel moment-based control pulse design technique for robust quantum state generation in symmetric spin systems with parameter uncertainties.

Findings

Successfully generates GHZ and W states in simulations.

Demonstrates robustness against electromagnetic field uncertainties.

Utilizes a moment quantization approach for control design.

Abstract

In this work, we consider a parameterized Ising model with long-range symmetric pairwise interactions on a network of spin $\frac{1}{2}$ particles. The system is designed with symmetric dynamics, allowing for the reduction of the state space to a subspace defined by the set of Dicke states. We propose a method for designing robust electromagnetic amplitude pulses based on a moment quantization approach. The introduced parameter accounts for uncertainties in the electromagnetic field, resulting in a family of distinct Hamiltonians. By employing a discretized moment-based quantization technique, we design a control pulse capable of simultaneously steering an infinite collection of dynamical systems to compensate for parameter variations. This approach benefits from the duality between the infinite-dimensional parameterized system and its finite-dimensional trucnated moment dynamics. Simulation results demonstrate the efficacy of this method in achieving states of significant interest in quantum sensing, including the GHZ and W states.